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Interpolation is a statistical strategy for estimating an unknown price or possible yield of an asset using related known variables. Interpolation is done by using other known values that are in the same order as the unknown value.
Interpolation is, at its core, a straightforward mathematical notion. If a group of data points has a relatively constant trend, one may confidently predict the value of the set for points that haven’t been computed. Investors and stock analysts typically use interpolated data points to build a line chart. These charts, which are a key aspect of technical analysis, enable them to visualise fluctuations in the price of assets.
• Investors utilize interpolation, a basic mathematical procedure, to predict an unknown price or possible yield of a security or asset based on comparable known values.
• Investors can estimate unknown values and put them on charts depicting a stock’s price movement over time by employing a consistent trend across a group of data points.
• One critique of interpolation in investment research is that it is imprecise and does not always reflect the volatility of publicly traded equities.
Interpolation is a technique used by investors to construct new estimated data points between known data points on a graph. Interpolation is commonly employed on charts that depict the price action and volume of a securities. While computer techniques are now widely used to produce these data points, interpolation is not a new notion. Early astronomers in Mesopotamia and Asia Minor employed interpolation to fill in gaps in their observations of the motions of the planets.
Interpolation Example
A linear interpolation is the simplest and most used type of interpolation. When trying to predict the value of a security or interest rate for a point when there is no data, this form of interpolation comes in handy.
Let’s say we’re following the price of a security over a period of time. The line on which the value of the security is tracked will be referred to as the function f. (x). We’d map the stock’s current price over a succession of points that represent different times in time. xAug, xOct, and xDec, or x1, x3, and x5, are the mathematical representations of f(x) for August, October, and December, respectively.
We could wish to know the value of the security during September, a month for which we don’t have any data, for a variety of reasons. To estimate the value of f(x) at plot point xSep, or x2 that comes within the existing data range, we might apply a linear interpolation approach.
The formula
Y = Y1 + (Y2 – Y1)/(X2 – X1) * (X * X1)
As we learnt in the definition above, it aids in determining a value depending on other sets of values, as seen in the formula above: –
• X and Y are unknown figures that will be determined based on the other variables provided.
• Y1, Y2, X1, and X2 are each given a set of variables to aid in the determination of an unknown value.
Example:
Calculate the unknown value using the interpolation formula from the given set of data. Calculate the value of Y when X value is 60.
X | Y |
10 | 0 |
30 | 40 |
50 | 80 |
70 | 120 |
90 | 160 |
Solution:
The value of Y can be derived when X is 60 with the help of Interpolation as follows: –
Here X is 60, Y needs to be determined. Also,
X1 | 50 |
Y1 | 80 |
X2 | 70 |
Y2 | 120 |
So, the Calculation of Interpolation will be –
Y= Y1 + (Y2-Y1)/(X2-X1) * (X-X1)
=80 + (120-80)/(70-50) * (60-50)
=80 + 40/20 *10
= 80+ 2*10
=80+20
Y = 100
Methods of interpolation
Interpolation methods come in a variety of shapes and sizes. They are as follows:
Linear Interpolation Approach — In the case of curves, this method applies a separate linear polynomial between each pair of data points, or among sets of three points in the case of surfaces.
The Nearest Neighbour Method – it replaces the value of an interpolated point with the value of the data point closest to it. As a result, this procedure generates no new data points.
Cubic Spline Interpolation Approach — In the case of curves, this method fits a distinct cubic polynomial between each pair of data points, or between sets of three points in the case of surfaces.
Piecewise Cubic Hermite Interpolation — This approach is also known as Shape-Preservation Method (PCHIP). The data’s monotonicity and form are preserved. It’s exclusively for curves.
Thin-plate Spline Approach — This method uses smooth surfaces that are good at extrapolating. It’s just good for surfaces.
Conclusion
Interpolation is most commonly used to assist users, such as scientists, photographers, engineers, and mathematicians, in determining what data may exist outside of their acquired data. Interpolation is commonly used outside of mathematics to scale pictures and alter the sample rate of digital data.
